2(n-2)-5(n-5)=4(n-8)-2(n-2)

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Solution for 2(n-2)-5(n-5)=4(n-8)-2(n-2) equation: 


Simplifying
2(n + -2) + -5(n + -5) = 4(n + -8) + -2(n + -2)

Reorder the terms:
2(-2 + n) + -5(n + -5) = 4(n + -8) + -2(n + -2)
(-2 * 2 + n * 2) + -5(n + -5) = 4(n + -8) + -2(n + -2)
(-4 + 2n) + -5(n + -5) = 4(n + -8) + -2(n + -2)

Reorder the terms:
-4 + 2n + -5(-5 + n) = 4(n + -8) + -2(n + -2)
-4 + 2n + (-5 * -5 + n * -5) = 4(n + -8) + -2(n + -2)
-4 + 2n + (25 + -5n) = 4(n + -8) + -2(n + -2)

Reorder the terms:
-4 + 25 + 2n + -5n = 4(n + -8) + -2(n + -2)

Combine like terms: -4 + 25 = 21
21 + 2n + -5n = 4(n + -8) + -2(n + -2)

Combine like terms: 2n + -5n = -3n
21 + -3n = 4(n + -8) + -2(n + -2)

Reorder the terms:
21 + -3n = 4(-8 + n) + -2(n + -2)
21 + -3n = (-8 * 4 + n * 4) + -2(n + -2)
21 + -3n = (-32 + 4n) + -2(n + -2)

Reorder the terms:
21 + -3n = -32 + 4n + -2(-2 + n)
21 + -3n = -32 + 4n + (-2 * -2 + n * -2)
21 + -3n = -32 + 4n + (4 + -2n)

Reorder the terms:
21 + -3n = -32 + 4 + 4n + -2n

Combine like terms: -32 + 4 = -28
21 + -3n = -28 + 4n + -2n

Combine like terms: 4n + -2n = 2n
21 + -3n = -28 + 2n

Solving
21 + -3n = -28 + 2n

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-2n' to each side of the equation.
21 + -3n + -2n = -28 + 2n + -2n

Combine like terms: -3n + -2n = -5n
21 + -5n = -28 + 2n + -2n

Combine like terms: 2n + -2n = 0
21 + -5n = -28 + 0
21 + -5n = -28

Add '-21' to each side of the equation.
21 + -21 + -5n = -28 + -21

Combine like terms: 21 + -21 = 0
0 + -5n = -28 + -21
-5n = -28 + -21

Combine like terms: -28 + -21 = -49
-5n = -49

Divide each side by '-5'.
n = 9.8

Simplifying
n = 9.8

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